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We construct a simple nonsingular cosmological model in which the currently observed expansion phase was preceded by a contraction. This is achieved, in the framework of pure general relativity, by means of a radiation fluid and a free scalar field having negative energy. We calculate the power spectrum of the scalar perturbations that are produced in such a bouncing model under the assumption of initial vacuum state for the quantum field associated with the hydrodynamical perturbation. The matching conditions applying to this bouncing model are derived and shown to be different from those in the case of a sharp transition. We show that if our bounce transition is smoothly connected to a slowly contracting phase, this provides a new way to generate a scale invariant power spectrum.
Peter et al. (Wed,) studied this question.